bool TTPAttack::run( const TTPTuple& d )
{
Word original_z = d.z;
// Convert the tuples
vector<ThLeftNormalForm> theTuple( d.WL.size()+d.WR.size() );
for ( int i=0;i<d.WL.size();i++) {
theTuple[i] = ThLeftNormalForm( BraidGroup( N ) , d.WL[i] );
theTuple[i].setPower( theTuple[i].getPower() % 2 );
}
for ( int i=0;i<d.WR.size();i++) {
theTuple[i+d.WL.size()] = ThLeftNormalForm( BraidGroup( N ) , d.WR[i] );
theTuple[i+d.WL.size()].setPower( theTuple[i+d.WL.size()].getPower() % 2 );
}
// execute attack
// run LBA to restore delta values
reduceDeltaLBA( theTuple );
// Test LBA
bool DelatLBA_succ = true;
for ( int i=0;i<d.WL.size();i++) {
if ( shortenBraid(N,theTuple[i].getWord()*-d.WL[i]).length() > 0)
DelatLBA_succ = false;
// cout << "F";
// else
// cout << "S";
}
for ( int i=0;i<d.WR.size();i++) {
if ( shortenBraid(N,theTuple[i+d.WL.size()].getWord()*-d.WR[i]).length() > 0)
DelatLBA_succ = false;
// cout << "F";
// else
// cout << "S";
}
if ( !DelatLBA_succ )
cout << "WARN!!! Delta LBA FAILED!" << endl;
// return oneOfSSSReps( d.WL.size(), d.WR.size(), theTuple );
// TTPTuple red_T;
//return simpleLBA(d.WL.size(), d.WR.size(), theTuple, original_z );
return LBA(d.WL.size(), d.WR.size(), theTuple, original_z );
}
pair< ThLeftNormalForm , ThLeftNormalForm > ThLeftNormalForm::cycle( ) const
{
if( theDecomposition.empty( ) )
return pair< ThLeftNormalForm , ThLeftNormalForm >( *this , ThLeftNormalForm( theRank ) );
ThLeftNormalForm result = *this;
Permutation first = *(theDecomposition.begin( ));
if( theOmegaPower%2!=0 )
first = first.flip( );
result.theDecomposition.push_back( first );
result.theDecomposition.pop_front( );
result.adjust( );
return pair< ThLeftNormalForm , ThLeftNormalForm >( result , ThLeftNormalForm(first) );
}
pair< ThLeftNormalForm , ThLeftNormalForm > ThLeftNormalForm::decycle( ) const
{
if( theDecomposition.empty( ) )
return pair< ThLeftNormalForm , ThLeftNormalForm >( *this , ThLeftNormalForm( theRank ) );
ThLeftNormalForm result = *this;
Permutation last = *(--theDecomposition.end( ));
if( theOmegaPower%2==0 )
result.theDecomposition.push_front( last );
else
result.theDecomposition.push_front( last.flip( ) );
result.theDecomposition.pop_back( );
result.adjust( );
return pair< ThLeftNormalForm , ThLeftNormalForm >( result , -ThLeftNormalForm(last) );
}
pair< bool , ThLeftNormalForm > ThLeftNormalForm::areConjugate( const ThLeftNormalForm& rep ) const
{
NF pr1 = *this;
reverse( pr1 );
ThRightNormalForm rightNF1 = pr1;
NF pr2 = rep;
reverse( pr2 );
ThRightNormalForm rightNF2 = pr2;
pair< bool , ThRightNormalForm > res = rightNF1.areConjugate( rightNF2 );
NF conj = res.second;
reverse( conj );
return pair< bool , ThLeftNormalForm >( res.first , -ThLeftNormalForm(conj) );
}
pair< bool , ThLeftNormalForm >
ThLeftNormalForm::ussConstructionIteration( map< ThLeftNormalForm , pair< ThLeftNormalForm , int > >& uss_new1 ,
map< ThLeftNormalForm , pair< ThLeftNormalForm , int > >& uss_checked1 ,
const map< ThLeftNormalForm , pair< ThLeftNormalForm , int > >& uss_new2 ,
const map< ThLeftNormalForm , pair< ThLeftNormalForm , int > >& uss_checked2 ) const
{
const Permutation omega = Permutation::getHalfTwistPermutation( theRank );
const pair< ThLeftNormalForm , pair< ThLeftNormalForm , int > > pr = *uss_new1.begin( );
uss_checked1[pr.first] = pr.second;
uss_new1.erase( uss_new1.begin( ) );
// 1. compute the set of simple summit conjugators
set< pair< Permutation , bool > > conj = pr.first.getSimpleUltraConjugators( pr.second.second );
for( set< pair< Permutation , bool > > ::iterator it=conj.begin( ) ; it!=conj.end( ) ; ++it ) {
// Conjugate the current element
ThLeftNormalForm conj( (*it).first );
ThLeftNormalForm res = -conj * pr.first * conj;
// Check if the element is new
if( uss_new1.find( res )!=uss_new1.end( ) ||
uss_checked1.find( res )!=uss_checked1.end( ) )
continue;
// Compute new conjugator
ThLeftNormalForm new_conjugator = pr.second.first * conj;
pair< bool , ThLeftNormalForm > traj_add_result =
ussAddTrajectory( res , new_conjugator , uss_new1 , uss_checked1 , uss_new2 , uss_checked2 );
if( traj_add_result.first )
return traj_add_result;
}
return pair<bool,ThLeftNormalForm>( false , ThLeftNormalForm( theRank ) );
}
pair< bool , ThLeftNormalForm > ThLeftNormalForm::areConjugate_uss( const ThLeftNormalForm& rep , int time_sec_bound ) const
{
if( theRank!=rep.theRank )
return pair< bool , ThLeftNormalForm >( false , ThLeftNormalForm( theRank ) );
int init_time = time(0);
// 1. find representative of SSS1
triple< ThLeftNormalForm , ThLeftNormalForm , int > tr1 = findUSSRepresentative( );
triple< ThLeftNormalForm , ThLeftNormalForm , int > tr2 = rep.findUSSRepresentative( );
// Infimum and supremum of nf1 and nf2 must be the same
if( tr1.first.theOmegaPower !=tr2.first.theOmegaPower ||
tr1.first.theDecomposition.size( )!=tr2.first.theDecomposition.size( ) )
return pair< bool , ThLeftNormalForm >( false , ThLeftNormalForm( theRank ) );
// If nf1==nf2 then we are lucky and can stop
if( tr1.first==tr2.first )
return pair< bool , ThLeftNormalForm >( true , tr2.second * -tr1.second );
// 3. construct ultra summit sets
map< ThLeftNormalForm , pair< ThLeftNormalForm , int > > uss_new1;
map< ThLeftNormalForm , pair< ThLeftNormalForm , int > > uss_checked1;
map< ThLeftNormalForm , pair< ThLeftNormalForm , int > > uss_new2;
map< ThLeftNormalForm , pair< ThLeftNormalForm , int > > uss_checked2;
ussAddTrajectory( tr1.first , tr1.second , uss_new1 , uss_checked1 , uss_new2 , uss_checked2 );
pair< bool , ThLeftNormalForm > traj_add_result =
ussAddTrajectory( tr2.first , tr2.second , uss_new2 , uss_checked2 , uss_new1 , uss_checked1 );
if( traj_add_result.first )
return pair< bool , ThLeftNormalForm >( true , -traj_add_result.second );
// uss_new1[tr1.first] = pair< ThLeftNormalForm , int >( tr1.second , tr1.third );
// uss_new2[tr2.first] = pair< ThLeftNormalForm , int >( tr2.second , tr2.third );
for( int i=0 ; i<1000000 && uss_new1.size( ) && uss_new2.size( ) ; ++i ) {
// Check if we have time to proceed
int cur_time = time(0);
if( cur_time-init_time>time_sec_bound )
return pair< bool , ThLeftNormalForm >( false , ThLeftNormalForm( theRank ) );
pair< bool , ThLeftNormalForm > pr = ussConstructionIteration( uss_new1 , uss_checked1 , uss_new2 , uss_checked2 );
if( pr.first ) {
// cout << "Size: " << uss_new1.size()+uss_checked1.size() << " - " << uss_new2.size()+uss_checked2.size() << endl;
return pair< bool , ThLeftNormalForm >( true , pr.second );
}
// Check if we have time to proceed
cur_time = time(0);
if( cur_time-init_time>time_sec_bound )
return pair< bool , ThLeftNormalForm >( false , ThLeftNormalForm( theRank ) );
pr = ussConstructionIteration( uss_new2 , uss_checked2 , uss_new1 , uss_checked1 );
if( pr.first ) {
// cout << "Size: " << uss_new1.size()+uss_checked1.size() << " - " << uss_new2.size()+uss_checked2.size() << endl;
return pair< bool , ThLeftNormalForm >( true , pr.second.inverse( ) );
}
}
return pair< bool , ThLeftNormalForm >( false , ThLeftNormalForm( theRank ) );
}
